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Robust stability conditions for feedback interconnections of distributed-parameter negative imaginary systems

Khong, Sei Zhen LU ; Petersen, Ian R. and Rantzer, Anders LU (2018) In Automatica 90. p.310-316
Abstract

Sufficient and necessary conditions for the stability of positive feedback interconnections of negative imaginary systems are derived via an integral quadratic constraint (IQC) approach. The IQC framework accommodates distributed-parameter systems with irrational transfer function representations, while generalising existing results in the literature and allowing exploitation of flexibility at zero and infinite frequencies to reduce conservatism in the analysis. The main results manifest the important property that the negative imaginariness of systems gives rise to a certain form of IQCs on positive frequencies that are bounded away from zero and infinity. Two additional sets of IQCs on the DC and instantaneous gains of the systems are... (More)

Sufficient and necessary conditions for the stability of positive feedback interconnections of negative imaginary systems are derived via an integral quadratic constraint (IQC) approach. The IQC framework accommodates distributed-parameter systems with irrational transfer function representations, while generalising existing results in the literature and allowing exploitation of flexibility at zero and infinite frequencies to reduce conservatism in the analysis. The main results manifest the important property that the negative imaginariness of systems gives rise to a certain form of IQCs on positive frequencies that are bounded away from zero and infinity. Two additional sets of IQCs on the DC and instantaneous gains of the systems are shown to be sufficient and necessary for closed-loop stability along a homotopy of systems.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Distributed-parameter systems, Integral quadratic constraints, Negative imaginary systems, Robust feedback stability
in
Automatica
volume
90
pages
7 pages
publisher
Pergamon
external identifiers
  • scopus:85041481692
ISSN
0005-1098
DOI
10.1016/j.automatica.2017.09.010
language
English
LU publication?
yes
id
e72b6397-8892-4a31-8d7c-f308b5fa7266
date added to LUP
2018-02-20 10:33:22
date last changed
2018-05-29 12:05:03
@article{e72b6397-8892-4a31-8d7c-f308b5fa7266,
  abstract     = {<p>Sufficient and necessary conditions for the stability of positive feedback interconnections of negative imaginary systems are derived via an integral quadratic constraint (IQC) approach. The IQC framework accommodates distributed-parameter systems with irrational transfer function representations, while generalising existing results in the literature and allowing exploitation of flexibility at zero and infinite frequencies to reduce conservatism in the analysis. The main results manifest the important property that the negative imaginariness of systems gives rise to a certain form of IQCs on positive frequencies that are bounded away from zero and infinity. Two additional sets of IQCs on the DC and instantaneous gains of the systems are shown to be sufficient and necessary for closed-loop stability along a homotopy of systems.</p>},
  author       = {Khong, Sei Zhen and Petersen, Ian R. and Rantzer, Anders},
  issn         = {0005-1098},
  keyword      = {Distributed-parameter systems,Integral quadratic constraints,Negative imaginary systems,Robust feedback stability},
  language     = {eng},
  month        = {04},
  pages        = {310--316},
  publisher    = {Pergamon},
  series       = {Automatica},
  title        = {Robust stability conditions for feedback interconnections of distributed-parameter negative imaginary systems},
  url          = {http://dx.doi.org/10.1016/j.automatica.2017.09.010},
  volume       = {90},
  year         = {2018},
}